### Impacto

Herrero, Miguel A. and Velázquez, J.J. L.
(1996)
*Singularity patterns in a chemotaxis model.*
Mathematische Annalen, 306
(1).
pp. 583-623.
ISSN 0025-5831

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## Abstract

The authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time. Such a finite-time blow-up of solutions implies chemotactic collapse, namely, concentration of species to form sporae. The model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity, which has the form ut=Δu−χ(uv), 0=Δv+(u−1), on ΩR2, where Ω is an open disc with no-flux (homogeneous Neumann) boundary conditions. The initial conditions are continuous functions u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 for xΩ. Under these conditions, the authors prove there exists a radially symmetric solution u(r,t) which blows up at r=0, t=T<∞. A specific description of such a solution is presented. The authors also discuss the strong similarity between the chemotactic model they study and the classical Stefan problem.

Item Type: | Article |
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Uncontrolled Keywords: | Blow-up; equations; radial solutions; chemotactic collapse |

Subjects: | Medical sciences > Biology > Biomathematics Sciences > Mathematics > Differential equations |

ID Code: | 17199 |

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Deposited On: | 26 Nov 2012 09:36 |

Last Modified: | 07 Feb 2014 09:43 |

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